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%I #15 Feb 06 2022 11:02:56
%S 1,1,7,140,5254,318854,28455182,3506576856,570360248856,
%T 118356589567440,30512901324706608,9566812017770347152,
%U 3584662956711860108352,1581905384865801328253712,812047187127758913474118032,479763784808095613489811245568
%N a(n) = Sum_{k=0..n} k! * k^k * Stirling1(n,k).
%F E.g.f.: Sum_{k>=0} (k * log(1+x))^k.
%F a(n) ~ exp(-exp(-1)/2) * n! * n^n. - _Vaclav Kotesovec_, Feb 06 2022
%t a[0] = 1; a[n_] := Sum[k! * k^k * StirlingS1[n, k], {k, 1, n}]; Array[a, 16, 0] (* _Amiram Eldar_, Feb 06 2022 *)
%o (PARI) a(n) = sum(k=0, n, k!*k^k*stirling(n, k, 1));
%o (PARI) my(N=20, x='x+O('x^N)); Vec(serlaplace(sum(k=0, N, (k*log(1+x))^k)))
%Y Cf. A006252, A305819, A320083, A350721, A350725, A351281.
%K nonn
%O 0,3
%A _Seiichi Manyama_, Feb 06 2022
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